The first quake, a magnitude 5.8, struck at 10:11 p.m, and had a depth of 15 km (9.3 miles) with its epicenter in Hualien county on Taiwan's eastern coast, the bureau said.
The second quake, measuring 6.2 on the Richter scale, hit a three minutes later at 10:14. The epicenter of the second quake was 20.2 kilometers southwest of Hualien County Hall, at a shallow depth of 13.9 kilometers.
There have been no reports of damage or casualties from the earthquakes.